This paper addresses the optimal design of shell-and-tube heat exchangers via a mathematical programming approach. It is shown that it is possible to develop a design model for shell-and-tube heat exchangers that takes into account some important construction variables: number of tubes, number of passes, internal and external tube diameters, tube arrangement pattern, number of baffles, head type, and fluid allocation (i.e., the allocation of the fluid streams to the shell or tubes). The model is based on generalized disjunctive programming and is optimized with a mixed-integer nonlinear programming reformulation to determine the heat-exchanger design that minimizes the total annual cost accounting for area and pumping expenses. Examples are presented to illustrate the model performance.